Tony Abbott is Australia’s 28th prime minister after a decisive swing to his Liberal National party Coalition – while Kevin Rudd has stood aside as Labor leader, taking solace in a party defeat that was not the rout widely predicted.

Tony Abbott claimed victory in front of ecstatic supporters at the Sydney Four Seasons hotel, declaring: “Australia is under new management and Australia is once again open for business.”

He promised his government would “be competent and trustworthy”, would “purposefully and steadfastly and methodically … set about delivering on our commitments” and would govern for everyone.

Rudd had emerged a little earlier to concede defeat to the Labor crowd at the Gabba cricket ground in Brisbane – so buoyed by the audience's cheering after a better-than-expected result that his first words were: “Jeez, I thought we’d lost …”

He told them he would be stepping down as Labor leader. “I gave it my all but it was not enough for us to win. … my responsibility has been to retain Labor as a fighting force for the future so we can unite behind the next leader of our party.

“I am proud that despite all the prophets of doom we have preserved our federal parliamentary Labor party as a viable fighting force for the future. … despite the pundits we appear to have held every seat in Queensland, every cabinet minister has been returned,” he said.

The nationwide swing of just over 3% against the ALP disguised huge variations around the nation, with 10% swings in Tasmania, a 4% swing in Victoria and a 3% swing in New South Wales, translating into a probable loss of 18 or 19 seats.

But Labor incurred only tiny swings in Rudd’s home state of Queensland, where it may have lost only two seats and where the mining billionaire Clive Palmer attracted 11% of the primary vote with a well-financed campaign for his Palmer United party.

Sorry, your browser is unable to play this video.

Kevin Rudd concedes defeat and resigns at Labor leader.

Tony Abbott will face a difficult Senate. As the count stood on Saturday night it was unclear whether the Greens would retain the balance of power with a net gain in senators or whether it would shift to an assortment of right and centrist senators, including the independent Nick Xenophon, a second candidate from his ticket, possibly two candidates from the Palmer United party in Queensland and Tasmania, and the already sitting DLP senator John Madigan.

Labor will face the task of choosing a new leader in the wake of the Gillard-Rudd era, with the unpopular party reform rules imposed by Rudd after he returned to the leadership requiring a lengthy grassroots ballot process if there is more than one candidate.

The most likely future Labor leader, Bill Shorten, said it was “a difficult evening but I feared it could have been worse”, saying he thought Rudd had done “a good job in helping Labor candidates to be returned”.

The outgoing Labor treasurer, Chris Bowen, another possible future leader who won his seat despite fears it might fall, said it was a better result for Labor than “might have been expected six months ago” and provided a good base for the party to rebuild.

The election threw up some wildcard results. Palmer himself appeared to have a chance of winning the Queensland coastal seat of Fairfax. The Coalition frontbencher Sophie Mirabella was fighting to hold her Victorian rural seat of Indi, where she was being challenged by a strong independent, Cathy McGowan. The stumbling Liberal candidate Jaymes Diaz failed to win the New South Wales seat of Greenway despite swings towards the Coalition in the seats surrounding. And the Greens' Adam Bandt retained the party’s only lower house seat of Melbourne with a 10% swing.

Abbott has been a relentlessly negative opposition leader who won the job with a pledge not to recognise Labor’s 2007 mandate to implement its emissions trading scheme, but who now promises a conflict-weary electorate calm, stable, “grown-up” government while demanding the upper house recognise his electoral mandate to immediately repeal the carbon tax.

Labor ousted Julia Gillard in favour of Rudd at the last minute on the calculation that Rudd’s higher popularity ratings would “save the party’s furniture”, and as the count progressed it seemed this would be the case in Queensland. However a slew of Labor MPs appeared set to lose their seats in other states, with at least five losses in NSW, including the assistant treasurer, David Bradbury, three losses in each of Tasmania and Victoria and one loss in South Australia.

The Labor MPs losing on Saturday night join a long list of Labor luminaries who did not recontest their positions this election, including Chris Evans, Nicola Roxon, Robert McClelland, Martin Ferguson, Greg Combet, Stephen Smith, Craig Emerson and Simon Crean.

Labor ran a largely negative campaign based on the allegation that Abbott would bring in European-style austerity via spending cuts. But Abbott switched to a more statesmanlike demeanour during the five-week campaign, eschewing Labor’s predicted drastic cuts despite having constantly claimed that Australia was facing a “budget emergency”.

Sorry, your browser is unable to play this video.

What it all means: post-election analysis with Lenore Taylor, Simon Jackman and Katharine Murphy.

A huge challenge for Abbott will be the upper house, where the Coalition will not win control in its own right and is likely to have to rely on a collection of centrist and centre-right independents once the newly elected senators take their seats next July.

Abbott, a Rhodes scholar, seminarian, cement plant manager, journalist and political adviser, has spent four years as opposition leader and forced Labor into minority government at the last election in 2010.

His time as opposition leader has been marked by his campaign against Labor’s carbon pricing scheme, Labor’s gradual acceptance of the Coalition view that Australia needs harsh policies to stop asylum seekers arriving by boat, and a political contest about whether Labor’s $42bn in stimulus spending in response to the 2008 financial crisis “saved” Australia’s economy or contributed to what Abbott has claimed is a “budget emergency”.

As victory appeared increasingly assured, Abbott had allowed himself to ponder out loud the burdens of the high office which for weeks he had looked certain to finally attain.

"If you look at people like John Howard, if you look at people like Bob Hawke, they certainly grew throughout their public life as opposition leader, as prime minister. Whatever faults and mistakes the pair of them might have made, by the time they were in the prime of their life as prime minister they were different, almost ennobled figures from those they had been quite a few years earlier. That's what high office does. It's a burden but it also does act to bring the best out of the better people who have got those jobs."

His biggest election promise was a more generous paid parental leave scheme, offering mothers up to $75,000 for six months' leave at an annual cost of $5.5bn – a policy deeply unpopular with his own party and the business community, but which Abbott cites as evidence that he and his party “get” the lives and needs of modern women, despite Gillard’s now-famous speech labelling him a misogynist.

Abbott is promising $11bn for city roads in a pitch to suburban commuters angry about traffic jams. Abbott says he aims “to be an infrastructure prime minister who puts bulldozers on the ground and cranes into our skies”.

He will cut company tax by 1.5%, except for the 3,000 largest businesses which will continue to pay the existing 30% tax rate, but with the final 1.5% now termed a “temporary levy” to help to pay for the expensive parental leave plan.

Labor has failed to win many plaudits for Australia’s relatively strong economy, which has recorded 22 years of uninterrupted economic growth, and boasts low unemployment and relatively low interest rates. Both major parties accept that voters feel under cost of living pressure, despite studies showing the average Australian household is in fact $5,302 better off in real terms than it was in 2008.